Question

Calculate the area of the designed region in Fig. common between the two quadrants of circles of radius $8cm$ each.

Answer 1

Area of shaded region $=$$2\times$ Area of segment $BD$
Considering the quadrant $ABD,$

Area of quadrant ABD$=\frac{\pi \times r^2}{4}$ $=\frac{1}{4}\times 3.14\times 8\times 8=50.24c{m}^2$
Area of $△$ABD $=\frac{1}{2}\times 8\times 8=32c{m}^2$
$\therefore$ Area of segment $BD$ $=$ Area of quadrant $ABD$ $-$ Area of $△ABD$
$=50.24-32=18.24c{m}^2$
$\therefore$ Area of shaded region $=2\times 18.24=36.48c{m}^2$